Production of flat conductor cables

ABSTRACT

The invention pertains to a method of transporting a flat conductor cable ( 1 ) to, between and from processing stations ( 2, 3 ) by means of drive rolls ( 4′, 4″; 5′, 5″; 6′, 6″ ).  
     The invention is characterized in that drive rolls ( 4′, 4″; 5′, 5″; 6′, 6″ ) are driven at differing tangential surface velocities.  
     The invention also pertains to a device for carrying out such a method.

[0001] The invention pertains to the production and equipping of flat conductor cables, in particular, to their movement in the course of producing, processing and equipping them. The invention pertains especially to a method for transporting a flat conductor cable to, between and from processing stations by means of drive rolls, to elaborations of this method and to a device for carrying out the method.

[0002] There are two types of flat conductor cables, laminated and extruded, both of which can be continuously produced and which are subjected to various processing steps at various sequential processing stations, either directly from the place where they are produced or from a drum on which they are temporarily stored. These various processing steps may be the removal of part of an insulating layer to form a window or the connection to some type of electronic element or to elements for handling or the like.

[0003] It is important that, while continuously passing through several stations, between which the drive rolls for the flat conductor cable are located, the velocity of the flat conductor cable between the stations is different [from one pair to another] and increases in the direction of movement. This results in the formation of humps, loops and the like, to the appearance of different conditions at the individual stations, and ultimately to the shutdown of the system by the monitoring system.

[0004] Not only does this problem occur if there are a great number of successively arranged stations, it always occurs if a great length of a flat conductor cable is to be processed all at once. Then these problems occur already for two processing stations with a total of three drive stations. Even intervening shutdown and “tightening” is only partially effective, since knowledge of the exact position of processing steps already performed on the flat conductor cable is lost.

[0005] Solving these problems is the task and the objective of the invention.

[0006] According to the invention, this objective is achieved in that the drive rolls are driven at different velocities and a slip clutch is provided between roll parts that contact the flat conductor cable and the drive elements. In this manner, a measurable and reproducible movement of the flat conductor cable is achieved, even across many processing stations.

[0007] As a function of the surface characteristics of the respective drive roll and the flat conductor cable, the contact pressure between drive roll and flat conductor cable, any existing contamination of the surfaces and other operating parameters, the slip clutch is to be calibrated such that it begins to slip before sliding friction between drive roll and flat conductor cable appears. This calibration can easily be done by a person skilled in the art with knowledge of the invention on the basis of the data sheets of the flat conductor cable and possibly a few additional experiments.

[0008] The invention is explained in greater detail below on the basis of the drawing.

[0009] Therein FIG. 1 shows a schematic representation of a production line and

[0010]FIG. 2 shows the schematic structure of a drive roll.

[0011]FIG. 1 shows purely schematically the movement of a flat conductor cable 1 in the area of two processing stations 2, 3. The movement of flat conductor cable 1 is accomplished by three drive stations 4, 5 and 6, of which, viewed in the direction of movement of the flat conductor cable, drive station 4 is the first and drive station 6 is the last one the flat conductor cable reaches. Each drive station 4, 5, 6 consists in essence of two rolls 4′, 4″; 5′, 5″ and 6′, 6″, of which the respective lower roll serves as drive roll 4′, 5′, 6′ and is therefore driven, while the respective upper roll serves as pressure roll 4″, 5″, 6″.

[0012] In the illustrated embodiment, final drive station 6 is driven directly by a motor or motor/gear assembly unit 7, while the other drive stations 4 and 5 are driven by means of toothed belts 8 and 9.

[0013]FIGS. 2 and 3 show, on the basis of a special embodiment, one of the two drive rolls 4′ or 5′. The outer surface 10, on which the flat conductor cable lies (FIG. 1) is connected to drive unit 11 (sprocket or direct drive) via an (adjustable) slip clutch 12. Thus it is assured that only a preset and preferably controllable torque can be transferred. This in turn implies that only a predetermined “drag force” is transferred to the flat conductor cable.

[0014] To ascertain the processing precision, which is dominated in the direction of movement by the kinematics of the drive train and the forces acting on the flat conductor cable, one must find an answer to the following questions:

[0015] 1. What forces and torques act on the flat conductor cable in the drive positions?

[0016] 2. What acceleration and velocity does the cable experience in the points of contact with the drive rolls?

[0017] 3. How does the cable behave between two rolls, or taking into account the entire kinematic train?

[0018] 4. What influence does the location of the position sensor have on processing precision?

[0019] For the controlled advancement of the flat conductor cable, two drive rolls, upstream and downstream of the production unit, are necessary for each application [of processing]. As long as the production units are not separated by buffers, the number of drive rolls is n+1, n indicating the number of separate processes.

[0020] Model of the Drive System

[0021] The drive system is implemented such that the last lower roll in the transport direction is driven free of play. The preceding rolls from the lower row are driven by toothed belts. The upper rolls lie on the lower ones with a slight initial tension so that a contact line results where they touch.

[0022] Due to manufacturing tolerances, both the sprockets and the cable drive rolls have differing outer diameters. In contrast to the case for gear pairs, it is necessary in order to ascertain the actual transmission ratio to consider the outer diameters of the sprockets as part of the flank clearance (the theoretical transmission ratio can, of course, be calculated from the effective diameters or the tooth count). Thereby, different circumferential velocities result at the cable drive rolls as long as this clearance in the respective direction is present. Depending on which of two successive rolls has the larger circumferential velocity, either an upset or a tensile zone is formed in the area between the rolls. It is obvious that a cable transport in which upset zones are formed is impermissible. Therefore, one can formulate the condition for a proper cable advancement as follows:

V_(i)<V₂<<V₂=circumferential velocity of the driven roll  (1)

[0023] The flat conductor cable must always be slightly tensioned! Proceeding from the angular velocity of the motor, one can derive the following expressions for the circumferential velocities of the cable drive rolls: ${(2)\quad V_{2}} = {{\frac{D_{n}}{2}\omega_{n}} = {{\frac{D_{n}}{2}\frac{\omega_{M}}{i_{G}}} = {R_{n}\frac{\omega_{M}}{i_{G}}}}}$ $V_{2} = {{\frac{D_{2}}{2}\omega_{2}} = {{\frac{D_{2}}{2}\frac{\omega_{n}}{i_{n2}}} = {{\frac{D_{2}}{2}\frac{\omega_{n}}{\frac{_{2}\quad}{_{n}\quad}}} = {{\frac{D_{2}}{2}\frac{_{n}}{_{2}}\frac{\omega_{M}}{i_{G}}} = {R_{2}\frac{_{n}}{_{2}}\frac{\omega_{M}}{i_{G}}}}}}}$ $V_{1} = {{\frac{D_{1}}{2}\omega_{1}} = {{\frac{D_{1}}{2}\frac{\omega_{2}}{i_{21}}} = {{\frac{D_{1}}{2}\frac{\omega_{2}}{\frac{_{1}\quad}{_{2}\quad}}} = {{\frac{D_{1}}{2}\frac{_{2}}{_{1}}\frac{_{n}\omega_{M}}{_{2}i_{G}}} = {R_{1}\frac{_{n}}{_{1}}\frac{\omega_{M}}{i_{G}}}}}}}$ ${{or}\quad {in}\quad {{general}:{\left( {2a} \right)\quad V_{i}}}} = {{\frac{D_{i}}{2}\omega_{i}} = {{\frac{D_{i}}{2}\frac{\omega_{i + 1}}{i_{{n + 1},i}}} = {{\frac{D_{i}}{2}\frac{\omega_{i + 1}}{\frac{_{i}\quad}{_{i + 1}\quad}}} = {{\frac{D_{i}}{2}\frac{_{n}}{_{i}}\frac{\omega_{M}}{i_{G}}} = {R_{i}\frac{_{n}}{_{i}}\frac{\omega_{M}}{i_{G}}}}}}}$

[0024] D_(i)=outer diameter of the ith cable drive roll

[0025] ω_(I)=angular velocity of the ith cable drive roll

[0026] ω_(M)=angular velocity of the motor

[0027] i_(G)=gear assembly transmission ratio

[0028] d_(i)=outer diameter of the sprocket

[0029] From the above formulas, it is evident that condition (1) can be satisfied by varying two parameters, namely the roll diameter D_(i) and the sprocket diameter d_(i).

[0030] The production processes do not take place in the direct environs of a roll, however, but rather in the middle between two rolls. Therefore, it is necessary to know the distribution of flat conductor cable velocity between the rolls in order to be able to synchronize the velocity of the process with that of the cable if desired.

[0031] Let us first consider the motion of the flat conductor cable only between two rolls i and i−1. The velocity of the cables at the rolls is known or can be determined from (2).

[0032] According to condition (1), the velocity increases continuously between the rolls. For the velocity of the cable at an arbitrary point between the rolls, one can write $\begin{matrix} {{{(3)\quad V} = {{V_{i - t} + {\frac{V_{i} - V_{i - 1}}{t_{1} - t_{m}}\left( {t - t_{0}} \right)\quad {Or}\quad {for}\quad t_{g}}} = 0}}{V = {V_{i - 1} + {\frac{V_{i} - V_{i - 1}}{t_{1}}t}}}} & \left( {3a} \right) \end{matrix}$

[0033] If one further considers that $t_{1} = {\frac{l}{\sim V} = {\frac{l}{V_{i - 1} + \frac{S}{t_{1}}} = {\frac{l}{V_{i - 1}\frac{1}{2}t_{1}\frac{\left( {V_{i} - V_{i - 1}} \right)}{t_{1}}} = {\frac{l}{V_{i - 1} + \frac{V_{1} - V_{i + 1}}{2}} = \frac{2l}{V_{i} + V_{i - 1}}}}}}$

[0034] one can express (3) solely as a function of t: ${\left( {3b} \right)\quad V} = {V_{i - 1}\frac{V_{l}^{2} - V_{l - i}^{2}}{2l}t}$

[0035] l distance between the rolls

[0036] t₁ time for movement of a point of the cable from roll i−1 to roll i

[0037] ˜V average velocity of a point of the cable from i−1 to i

[0038] S surface area of triangle V_(i−1)PV_(i).

[0039] Integrated in the interval 1₀−1, the differential form of (3b), dx/dt=( . . . )t, supplies the motion law of a point of the cable in its movement from point i−1 to i: ${{(4)\quad x}|_{0}^{i}} = {x_{0} + {V_{i - 1}t} + {\frac{V_{i}^{2} - V_{i - 1}^{2}}{4l}t^{2}}}$

[0040] In sum, the following can be stated for that which has been ascertained thus far:

[0041] 1. velocity of the cable in the rolls and the influence of roll and sprocket diameter on this velocity

[0042] 2. distribution of the cable velocity between 2 rolls

[0043] 3. motion law of the cable between 2 rolls.

[0044] Now, an answer must be found to the question of what power is necessary for the forward motion of the cable, or with what pressing force can normal operation be guaranteed.

[0045] The dynamic analysis of the drive/flat conductor cable system brings insight into the external forces acting on the flat conductor cable and their influence on the positional or processing precision and on the boundary conditions for a slip-free conveyance of the belt. First one must determine the drive force on the flat conductor cable. This force is collinear with the x-axis of the model. For this, it is necessary to ascertain the equivalent mass reduced to the x-axis. Presently the necessary pressing forces onto the flat conductor cable are determined, taking into account the resistance forces induced by processing and friction. Here following FIG. 2, one proceeds from the following constructive elaboration of the rolls (the justification for the approach follows in the presentation).

[0046] The equivalent mass can be ascertained by equating the kinetic energies of the model and of the actual system. We will conditionally divide the dynamic system in two—FFC [flat conductor cable] system and drive subsystem. Accordingly, for the kinetic energy of the two subsystems, one can write: ${(5)\quad E_{FR}} = {\sum\limits_{i = 1}^{n - 1}{\frac{1}{2}\left( {m_{FR},{l_{t} - V_{i,{j + 1}}^{2}}} \right)}}$

[0047] l_(i) distance between rolls i and i+1

[0048] ˜V average velocity of a point of the cable from i to i+1

[0049] m_(FFC) mass of FFC in kg/m

[0050] For the sake of simplicity, we substitute in (5) instead of ˜V->V_(i), thus ${\left( {5a} \right)\quad E_{FR}} = {{\sum\limits_{i = 1}^{n - 1}{\frac{1}{2}\left( {m_{FFC},{l_{i}V_{i}^{2}}} \right)\quad {{and}\quad (6)}\quad E_{A}}} = {E_{M} + E_{G} + {\sum\limits_{i = 1}^{n}E_{{RU}_{i}}} + {\sum\limits_{i = 1}^{n}E_{{RO}_{i}}} + {\sum\limits_{i = 1}^{n - 1}E_{{SR}_{i}}} + {\sum\limits_{i = 1}^{n - 1}E_{{ZR}_{i}}}}}$

[0051] E_(M)=kinetic energy of motor

[0052] E_(G)=KE of gear assembly

[0053] E_(OR)=KE of upper roll

[0054] E_(UR)=KE of lower roll

[0055] E_(SR)=KE of tension roll

[0056] E_(ZR)=KE of toothed belt $\begin{matrix} {{(6.1)\quad E_{M}} = {\frac{1}{2}J_{M}\omega_{M}^{2}}} \\ {{{(6.2)\quad E_{G}} = {\frac{1}{2}J_{G}\omega_{M}^{2}}}\quad} \\ {{(6.3)\quad E_{RO}} = {\frac{1}{2}{\sum\limits_{i = 1}^{n}{J_{{RO}_{i}}\omega_{{RO}_{i}}^{2}}}}} \\ {J_{RO} = {\frac{1}{2}\left\lbrack {{m_{Ratio}\left( {R_{{Rohr}_{2}}^{2} + R_{{Rohr}_{1}}^{2}} \right)} + {2{m_{t_{r}}\left( {R_{l_{\Delta}}^{2} + R_{l_{r}}^{2}} \right)}}} \right\rbrack}} \\ {\omega_{RO} = {\frac{V_{i}}{R_{RO}} = \frac{R_{{RO}_{i}},{r_{n}\omega_{M}}}{R_{{RO}_{i}},{r_{i}i_{ri}}}}} \end{matrix}$

[0057] The index L stands for the bearings, R_(Rui) and R_(Roi) concern the outer radius of the upper and lower rolls, r_(n) and r_(i) signify the radius of the corresponding sprocket. ${{(6.4)\quad E_{RO}} = {\frac{1}{2}{\sum\limits_{i = 1}^{n}J_{{RO}_{i}}}}},\omega_{{RO}_{i}}^{2}$ $J_{RU} = {{{\quad {{\frac{1}{2}\left\lbrack {{m_{Rohr}\left( {R_{Rohr}^{2} + R_{Rohr}^{2}} \right)} + {3{m_{L}\left( {R_{L_{A}}^{2} + R_{L_{1}}^{2}} \right)}} + {m_{D}\left( {R_{D_{A}}^{2} + R_{D1}^{2}} \right)} + {m_{GS}\left( {R_{{GS}_{1}}^{2} + R_{{CS}_{1}}^{2}} \right)} + {m_{ZS}\left( {R_{{ZS}_{A}}^{2} + R_{{ZS}_{i}}^{2}} \right)}} \right\rbrack}++}}{\frac{1}{2}\left\lbrack {m_{AXL}\left( {R_{{AXL}_{A}}^{2} + R_{{AXL}_{i}}^{2}} \right)} \right\rbrack}\omega_{{RU}_{i}}} = \frac{r_{n}\omega_{M}}{r_{i}i_{G}}}$

[0058] Indices: D—lid; GS—sliding disk; ZS—sprocket; AXL—axial bearings ${{(6.5)\quad E_{{SR}_{i}}} = {\frac{1}{2}{\sum\limits_{i = 1}^{n - 1}{{J_{SR}}_{i}\omega_{{SR}_{i}}^{2}}}}},{J_{{SR}_{i}} = {\frac{1}{2}{m_{{SR}_{i}}\left( {R_{{SR}_{i}}^{2} + R_{{SR}_{i}}^{2}} \right)}}}$ $\omega_{{SR}_{i}} = {\frac{V_{{ZR}_{i}}}{R_{{SR}_{i}}} = {{\frac{r_{i}}{R_{{SR}_{i}}}\omega_{{RU}_{i}}} = \frac{d_{n}\omega_{M}}{R_{{SR}_{i}}i_{G}}}}$ ${(6.6)\quad E_{{ZR}_{i}}} = {{\frac{1}{2}m_{{ZR}_{i}}{V_{ZR}^{2}.\quad {{Where}:{m_{{ZR}_{i}}\lbrack{kg}\rbrack}}}} = {\left( {{2l_{i}} + {\pi \quad d_{ZR}}} \right)\left( {\rho \left\lbrack \frac{kg}{m} \right\rbrack} \right)\begin{matrix} {{\rho - {{material}\quad {density}}}\quad} \\ {I_{i} - {{distance}\quad {between}\quad {two}\quad {rolls}}} \end{matrix}}}$ $V_{ZR} = \frac{d_{n}\omega_{M}}{i_{G}}$

[0059] Now, one can write for the equivalent mass M_(ä), reduced to the x-axis: $\begin{matrix} {M_{a} = {{\left( {J_{M} + J_{O}} \right)\frac{\omega_{M}^{2}}{V_{m}^{2}}} + {\frac{1}{V_{m}^{2}}\left\lbrack {{\sum\limits_{i = 1}^{n}E_{{\pi 0}_{i}}} + {\sum\limits_{i = 1}^{n}E_{{RU}_{i}}} + {\sum\limits_{i = 1}^{n - 1}E_{{SR}_{i}}} + {\sum\limits_{i = 1}^{n - 1}E_{{ZR}_{i}}}} \right\rbrack}}} & (7) \end{matrix}$

[0060] Taking into account formula (2) and neglecting the slight differences in the kinematic parameters of the rolls and the sprockets (all drive rolls in a series, as well as all sprockets and tension rolls have ideal masses, or equivalently equal outer diameters), i.e. ${\omega_{RU} = \frac{\omega_{M}}{i_{C}}},{\omega_{RO} = \frac{R_{RU}\omega_{M}}{R_{RO}i_{G}}},{V_{t} = V_{n}}$

[0061] one can rewrite the equivalent mass as follows: $M_{d}^{A} = {{\left( {J_{M} + J_{C}} \right)\frac{i_{G}^{2}}{R_{n}^{2}}} + {{\frac{i_{G}^{2}}{R_{n}^{2}\omega_{M}^{2}}\begin{bmatrix} {{n\quad J_{RO}\frac{R_{RU}^{2}\omega_{M}^{2}}{R_{RO}^{2}i_{\sigma}^{2}}} + {{nJ}_{RU}\frac{\omega_{M}^{2}}{i_{G}^{2}}} +} \\ {{\left( {n - 1} \right)J_{SR}\frac{R_{ZS}^{2}\omega_{M}^{2}}{R_{SR}^{2}i_{G}^{2}}} + {R_{ZS}^{2}\frac{\omega_{M}^{2}}{i_{G}^{2}}{\sum\limits_{i = 1}^{n - 1}m_{ZR}}}} \end{bmatrix}}++}}$ $\quad {{\frac{1}{V_{n}^{2}}{\sum\limits_{i = 1}^{n - 1}{m_{FFC}l}}},V_{i}^{2}}$ $\begin{matrix} {M_{\sigma}^{A} = {{\left( {J_{M} + J_{G}} \right)\frac{i_{G}^{2}}{R_{n}^{2}}} + {\frac{n}{R_{n}^{2}}\left\lbrack {{J_{RO}\frac{R_{RU}^{2}}{R_{RO}^{2}}} + J_{RU} + {\frac{n - 1}{n}J_{SR}\frac{R_{ZS}^{2}}{R_{SR}^{2}}} + {\frac{R_{ZS}^{2}}{n}{\sum\limits_{i = 1}^{n - 1}m_{{ZR}_{i}}}}} \right\rbrack}}} & \left( {7a} \right) \\ {M_{d} = {{m_{FR} \cdot {\sum\limits_{i = 1}^{n - 1}l_{i}}} + M_{\sigma}^{A}}} & \left( {7b} \right) \end{matrix}$

[0062] Thus, the system is reduced to the following model, where the entire mass is “concentrated” in FFC

[0063] The differential equation of the system is accordingly: $\begin{matrix} {{{{M_{n}\frac{^{2}x}{t^{2}}} + {\beta \frac{x}{t}}} = {{F_{A}\eta} - F_{r}}},} & (8) \end{matrix}$

[0064] where F_(A)—resulting drive force

[0065] F_(P)—resulting process force

[0066] β dx/dt=F_(R)—resulting friction force

[0067] η—efficiency of the entire drive system

[0068] The run-up time of the entire system can be ascertained from the motion equations $\begin{matrix} {{V = {V_{0} + {\frac{F_{A} - F_{r}}{M_{a}}t\quad {and}}}}} & (9) \\ {x = {x_{0} + {V_{0}t} + {\frac{F_{A} - F_{r}}{2M_{a}}t^{2}}}} & (10) \end{matrix}$

[0069] The advance constant K_(V) of the system is given by $\begin{matrix} {K_{i} = {{\phi_{n}R_{R}} = {{\frac{\phi_{M}}{i_{G}}R_{R}} = {\frac{2\pi}{i_{G}}{R_{R}\left\lbrack \frac{mm}{{Motor}\quad {revolution}} \right\rbrack}}}}} & (10) \end{matrix}$

[0070] For the sake of completeness, it will also be shown what drive forces are generated at the respective drive rolls. These forces can be approximately calculated by dividing the drive torque by the number of rolls and the radius of the drive roll: $\begin{matrix} {F_{A} = \frac{M_{A}i_{C}}{{nR}_{A}}} & (11) \end{matrix}$

[0071] The precise value is given by the expression: $\begin{matrix} {F_{A} = {M_{A}i_{G}\frac{r_{i}}{\sum\limits_{i = 1}^{n}r_{i}}\frac{1}{R_{{RU}_{i}}}{\prod\limits_{i = R}^{1}\quad \eta_{i}}}} & \left( {11a} \right) \end{matrix}$

[0072] where η_(i)—efficiency in the respective transmission stage; r_(i)—radius of respective sprocket.

[0073] It is clear from the presentation thus far that a continuous operation with a calculable behavior of the flat conductor cable is guaranteed only if it is subjected to a certain tension between two respective drive rolls. Thereby, an elastic force that does not increase linearly is generated in this area. The maximum value of this tensile force must be limited, however; otherwise the FFC may be stretched in the plastic range in some cases and narrow FFCs may even be destroyed. This value can be restricted in two ways: the pressing force between the rolls is set such that the FFC begins to slide on the corresponding drive roll when a limit value of tensile force is reached, or a slip clutch is provided at each drive roll except for the roll that is directly driven by the motor.

[0074] By means of this slip clutch, the drive torque transferred to the roll can be limited. When a predefined elastic elongation (or equivalently, elastic force) between two rolls is reached, one (or both) of the two begins to rotate at a different angular velocity from the driving sprocket. The slippage thus arises in the slip clutch and not between drive roll and cable. Thus a defined position of the cable with respect to the surface of each drive roll, and thus in space, is secured, which permits the processing of individual predetermined areas of the cables with high precision.

[0075] The conditions for a slip-free operation in the environs of a roll can be defined as follows, proceeding from the model of the drive system: $\begin{matrix} {{{\sum F_{X}}} \leq {{\mu_{0}R}\quad - {{Condition}\quad {for}\quad {slip}\text{-}{free}\quad {force}\quad {transfer}\quad {to}\quad {the}\quad {FFC}}}} & (12) \\ {{{\sum F_{X}}} \geq {{\frac{f}{r}R}\quad - {{Condition}\quad {for}\quad {r{olling}}\quad {of}\quad {the}\quad {drive}\quad {and}\quad {press}\quad {rolls}\quad {and}\quad {onto}\quad {the}\quad {FFC}}}} & (13) \end{matrix}$

[0076] where (without slip clutch): //insert A p 11//

[0077] f=coefficient of friction for rolling

[0078] μ₀=coefficient of friction for sliding

[0079] r=radius of roll

[0080] R=reaction force=F_(n)

[0081] For ΣF_(x)>0 and |ΣF_(x)|≧μ₀R, we have forward sliding, and backward sliding for ΣF_(x)<0 and |ΣF_(x)|≧μ₀R.

[0082] By installing the slip clutch one obtains a parameter with which the satisfaction of equations (12) and (13) can always be achieved. The equation of the forces on x changes as follows: $\begin{matrix} {{{\sum F_{X}} = {{F_{A} + {F_{{el}_{i,j,{+ 1}}}F_{{el}_{i,j,{+ 1}}}} - {F_{Kop}\quad {where}\quad t_{H}}} = {{run}\quad \text{-}{up}\quad {time}\quad {and}}}}\quad {{F_{{Kop}_{i}} = {k_{i}\frac{M_{{RU}_{i}}^{o} + M_{{RO}_{i}}^{o}}{R_{{RU}_{t}}}}},{M_{{{RU}{(o)}}_{i}}^{o} = {\frac{J_{{{RU}{(o)}}_{i}}}{t_{ll}}\omega_{{{RU}{(O)}}_{i}}}},{1 < k_{i} < \frac{M_{A_{i}}}{M_{{RU}_{i}}^{D} + M_{{RO}_{i}}^{D}}}}} & (13.1) \end{matrix}$

[0083] The clutch closing force F_(Zyl) is given by $\begin{matrix} {F_{Zyl} = {\frac{2R_{{RU}_{i}}F_{{KnD}_{i}}}{\mu \left( {R_{{GS}_{A_{i}}} + R_{{GSi}_{A_{i}}}} \right)} = {\frac{M_{{RU}_{i}}^{D} + M_{{RO}_{i}}^{D}}{\mu \left( {R_{{GS}_{A_{i}}} + R_{{GSi}_{i}}} \right)}2k}}} & (13.2) \end{matrix}$

[0084] In order to be able to set the driving of the flat conductor cable through the machine correctly, the elastic properties of the cable must be known. It should be ascertained in particular whether all cable widths can be processed with a constant setting of the limit value of elongation or whether an individual setting is necessary for slip-free operation in the cable strand, depending on the composition of the cable cross section. Since the elasticity of the cable is dominated by the copper, only this material is analyzed in the following analyses.

[0085] The spring constant c of a flat copper conductor is given by: $\begin{matrix} {c = \frac{ES}{l}} & (14) \end{matrix}$

[0086] with

[0087] E modulus of elasticity;

[0088] S cross sectional area;

[0089] l length of conductor

[0090] The spring constant of a flat conductor cable is accordingly given by the general formula $\begin{matrix} {c = \frac{{Eh}{\sum\limits_{i = 1}^{n}{\sum\limits_{j = 1}^{k}{ib}_{j}}}}{l}} & (15) \end{matrix}$

[0091] with

[0092] h height of conductor;

[0093] bj number of conductors;

[0094] i number of conductors of equal width.

[0095] The elastic force that arises between two conductors is dependent on the path x, that is, the time t. The origination process of the elastic force is illustrated by the diagram below:

[0096] δx=displacement of the point of contact of the wheels

[0097] Δx=absolute elongation of the cable

[0098] ε=relative elongation of the cable

[0099] e_(S)=specific elongation of the cable

[0100] l_(FFC)=unelongated length of the cable

[0101] l=distance between rolls

[0102] According to condition (1), V_(i+1) is always greater than V_(i), that is to say, the exiting end of the cable, i.e., the point of contact between rolls i+1, moves faster than the incoming one, that is to say, the point of contact between rolls i. This velocity difference results in the creation of a mechanical elongation in the cable strand that, as a function of the elastic constant of the cable, which in turn depends on the effective length of the cable, produces a lesser or greater elastic force. Due to the characteristics of the drive system, this force no longer increases linearly.

[0103] Let one consider the state of the cable strand at an arbitrary point in time t_(j). The cable has the following elastic parameters: Δx^(j), e_(i) ^(j), ε_(i) ^(j), t^(j) _(FFC). The part of the cable upstream of the rolls i has a relative (specific) elongation ε_(i−1) ^(j) (e_(i−1) ^(j)), and the strand downstream of the rolls i+1 a relative (specific) elongation ε_(i+1) ^(j)(e_(i) ^(j)).

[0104] During an infinitesimally small interval dt, the left end of the cable moves by δx^(j+1) _(i+1) and the right one by δx^(j+1) _(i) according to formula (2), and thus the parameters change as follows: $\begin{matrix} {{{\delta \quad x_{i}^{j + 1}} = {{{V_{i}(t)}t} + {\frac{{V_{i + 1}^{2}(l)} - {V_{l}^{2}(t)}}{4l}t^{2}}}},{{\delta \quad x_{i + 1}^{j + 1}} = {{{V_{i + 1}(t)}t} + {\frac{{V_{i + 2}^{2}(t)} - {V_{i + 1}^{2}(t)}}{4l}t^{2}}}}} & (16) \\ {{\Delta \quad x^{j + 1}} = {{\Delta \quad x^{j}} + {e_{i + 1}^{l}\delta \quad x_{i}^{j + 1}} - {e_{i}^{l}\delta \quad x_{t + 1}^{j + 1}}}} & (17) \\ {l_{FFC}^{j + 1} = {l - {\Delta \quad x^{j + 1}}}} & (18) \\ {{ɛ_{i}^{j + 1} = {\frac{l}{l_{FFC}^{j + 1}} - 1}},{e_{i}^{j + 1} = \frac{l_{FFC}^{j + 1}}{l}}} & (19) \end{matrix}$

[0105] Thus one can define the elastic force for each infinitesimally small time interval as

F _(cl) ^(i)=c_((x)Δx) ^(i), F_(cl) ^(j+1)=c_((i))Δx^(j+1) etc.,  (20)

generally,

F_(cl)(t)=c_((x)Δx(t))  (20a)

[0106] Summary of What Has Been Achieved Thus Far:

[0107] In the transport of the flat conductor cable through more than one roll, slip-free operation exists theoretically by idealizing the components of the kinematic chain, but cannot be realized in practice without additional measures, due to the manufacturing tolerances of the components and the elastic characteristics of the cable. In the design implementation of the machine plan, it is therefore necessary to seek solutions that eliminate the cable slippage in the rolls and thereby make the kinematic behavior of the cable predictable.

[0108] Such a solution is created by the invention. In the kinematic solution of the advancement drive according to the invention, the flat conductor cable moves through all the rolls without slippage. The velocities of the respective roll pairs are chosen, by appropriate selection of their diameter and that of their sprockets, such that the last driven roll in the direction of transport has the highest circumferential velocity, and each successive roll preceding it has a lower one. The friction forces on the FFC make sense only to the level of the drive forces and are determined by the contact pressure.

[0109] The differing circumferential velocities cause nonuniform displacements in the area between two respective rolls. These displacements bring about the creation of elastic forces in the respective cable strand. They increase nonlinearly so long as they do not exceed the lower friction force between one of the two roll pairs or if the difference of the products of the peripheral velocities and the specific elongations in the outlying areas goes toward zero. If the first occurs, the flat conductor cable should slip on the corresponding drive roll and thereby an equalization of the elastic forces takes place from both sides of the roll. Since this slippage is undesirable for the cable and the manufacturing precision, slip clutches are installed in all drive rolls up to the last one.

[0110] This or a similar compensation for the elastic forces takes place in the clutches, which suppresses the relative motion between cable and roll and guarantees a slippage-free operation. The forces, reduced to the x-axis, of the friction torques in the clutches are to be taken into account as resistance forces in acceleration of the system and as active forces during braking,

[0111] The last roll is the only one that is driven directly by the motor and without a slip clutch. The transmitted torques into the slip clutches are set to a value between the moment of inertia and the proportional drive torque on the roll. This peculiarity of the drive system guarantees a continuity of motion for the flat conductor cable and good deterministic characteristics for the overall system permitting a good estimation of the processing tolerances of the flat conductor cable, in addition to the correction of the position of the cable or the processing apparatuses by the control system.

[0112] The invention is not restricted to the illustrated and described embodiment, but can be modified in various ways. Instead of drive belts (toothed belts) it is also conceivable to use chains, gears or friction wheels, which can take over the function of the slip clutches under certain circumstances as well.

[0113] It is also possible to drive each drive roll at the predetermined rotational speed, the slip clutch in this case being constructed mechanically, as in the case described above, or electrically as a regulation of the drive torque.

[0114] The term “rotational speed” is always used in the description and the claims, but this applies in the strict sense only to drive rolls of mutually identical diameters; strictly speaking, one would have to use the respective tangential surface velocity as a comparative parameter, but this is familiar to the person skilled in the art. 

1. Method of transporting a flat conductor cable to, between and from processing stations by means of drive rolls, characterized in that the drive rolls are driven at differing tangential surface velocities.
 2. Method according to claim 1, characterized in that the flat conductor cable moves from drive rolls with lesser tangential surface velocity to drive rolls with greater tangential surface velocity.
 3. Method according to claim 1 or 2, characterized in that the drive torque of at least one drive roll is less than the frictional force between the surface of the drive roll and the flat conductor cable, multiplied by the radius of the drive roll.
 4. Device for carrying out the method according to one of the preceding claims, with drive rolls that set a flat conductor cable into motion, characterized in that the drive rolls are driven at differing tangential surface velocities.
 5. Device according to claim 4, characterized in that a slip clutch is provided between the surface and the drive system for at least one drive roll.
 6. Device according to claim 5, characterized in that the slip clutch is constructed mechanically, pneumatically or electrically.
 7. Device according to one of claims 4-6, characterized in that at least two drive rolls are driven with different torques.
 8. Device according to claims 7 and 5, characterized in that the differing torques are secured by differently constructed or calibrated slip clutches. 